The Modeling of growth process on the surface of crystal


  • R.L. Politanskyi Yuri Fedjkovych Chernivtsy National University, Chernivtsy, Ukraine
  • V.I. Gorbulik Yuri Fedjkovych Chernivtsy National University, Chernivtsy, Ukraine
  • I.T. Kogut Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
  • M.V. Vistak Danylo Halytsky Lviv National Medical University, Lviv, Ukraine



Monte Carlo method, crystal growth, analytical methods


The article is devoted to modelling the growth of thin films on the surfaces of crystals having a similar crystal structure with a small parameter of mismatch of the lattice of substances from which the film and the crystal substrate are formed. A review of modelling methods based on both analytical expressions and computational methods is made. A number of methods for modelling the most typical processes: surface formation in the form of pyramidal formations (so-called needle crystals), two-dimensional with initial islands of growth and three-dimensional uneven growth processes. To model the process of growth of needle crystals, it is proposed to use a method based on Gaussian statistics of surface height increments. The model of three-dimensional growth of the crystal surface, which uses the iterative algorithm of Foss, and which makes it possible to investigate the processes of stepped, uneven growth of crystals, is also considered. In contrast to stepwise growth, a model of submonolayer growth of a film based on the Monte Carlo method is considered. For submonolayer growth of the film, pseudo-random sequences are used, which simulate the initial arrangement of the nuclei of the nucleus of the next layer on the crystal surface. The computational characteristics of this method are determined, namely the dependence of the number of iterations on the initial surface filling coefficient.


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How to Cite

Politanskyi, R., Gorbulik, V., Kogut, I., & Vistak, M. (2022). The Modeling of growth process on the surface of crystal. Physics and Chemistry of Solid State, 23(2), 387–393.



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